An investigation into the parameters affecting the performance of tube mills : the behaviour of a single particle on a corrugated liner inside a rotating cylinder

Includes bibliographical references.This thesis is the second stage of a project to investigate the parameters affecting the performance of tube mills. The main topics that the project will cover are the motion of the mill charge and the wear characteristics of the mill charge and mill liners. Nates, in his thesis, performed a literature survey that highlighted the need for an investigation into the motion of a particle with emphasis on the response to changes in the coefficient of friction between the particle and the liner. Nates developed theoretical models for a particle moving on the inside of a rotating liner. The models developed were for a block and sphere moving on a flat liner. Although a better understanding of the motion of a particle was achieved, the models did not take all the variables into account. One of the assumptions made by Nates was that the particle was moving on a flat liner. This thesis concentrates on the motion of a particle on a corrugated liner in a rotating cylinder. Two formulations are presented that model the motion of a particle. The first model assumes that the particle being modelled is a block. The modelling of the particle as a block ensures that the particle does not roll. There are two possibilities as to the type of motion which the block can experience. The first possibility is where the block moves at the same velocity as the - rotating liner whilst the second possibility is where the block can slide relative to the rotating liner. Three different liner configurations were used in the investigation of the motion of a block. The second model assumes that the particle can move with pure rolling as well as with a combination of rolling and sliding. For pure rolling it is assumed that at the point of contact between the sphere and liner that there is no skidding or sliding. The governing equations for the model of a block on a corrugated liner are solved numerically using a Fourth-Order Runge-Kutta Method. The theoretical predictions of the motion of a block on a corrugated liner are presented - and discussed. The model for a sphere on a corrugated liner was derived but no attempt was made to solve it numerically. It is envisaged that the numerical solution of the model for a sphere will be included in the next stage of the project. An experimental investigation was done to validate the theoretical model for a block on a corrugated liner. Only two of the three liners used in the numerical investigation were tested. There was good correlation between the experimental results and the theoretical predictions. All the experimental results are presented and comparisons made between the theoretical predictions and the experimental results. The thesis is concluded with a discussion of trends and observations made during the investigation into the motion of a block on a corrugated liner, and it is shown that the model for a block on a corrugated liner does satisfactorily predict the response of the block to varying initial conditions. Suggestions are also made as to possible ways to improve and expand on the current models used to describe the motion of a mill charge